Grades 3-4 Video Solutions 2021-video 2021 3-4/24

Video Transcription

Problem number 24. Martin placed three different types of objects, hexagons, squares, and triangles  on sets of scales as shown. What does he need to put on the left-hand side of the third set of scales for these scales to balance? A, one square. B, two squares. C, one hexagon. D,  one triangle. Or E, two triangles. To solve a problem like this, we need to figure out  what shapes weigh the same as a certain number of other shapes, and then we can try to substitute.  Let's start by looking at the second scales right here. Each side has a hexagon on it. So, if we take a hexagon off each side, we take the same weight off each side, and we're left  with one triangle weighing the same as five squares. Let's write it down here. Triangle  the same as five squares. Next, we can substitute this into the first set of scales  to have hexagons on one side and squares on the other. So, instead of this triangle,  we can have five more squares.  Now, we know that two hexagons weigh the same as six squares. So, one hexagon  weighs the same as three squares. Now, let's look at the last set of scales, the one that the problem  asks about. On one side, we have three hexagons. On the other side, we have two triangles. They  don't evenly translate into each other's weight, but if one triangle was the same as five squares, two triangles weigh the same as ten squares.  And if one hexagon weighs the same as three squares, three hexagons weigh the same as nine  squares. So, if we add one square to the left side of the scales here, the scales will be balanced. Each side will weigh the same as ten squares. So, our answer is A. One square  needs to be added to the left-hand side of the third set of scales.

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